Fokker-Planck方程有限解析/Monte Carlo数值模拟方法

An Particle Tracing Scheme for Fokker-Planck Equation in Finite Analytic/Monte Carlo Methods

摘要

摘要:对白噪声驱动随机系统的Fokker-Planck方程进行约化，求得约化方程的解析解，使用局部解析解和MonteCarlo结合方法求解常系数Fokker-Planck方程，并与常系数Fokker-Planck方程的精确解进行对比，之后求解了变驱动力系统的行为. 数值模拟结果表明，有限解析/MonteCarlo结合的方法，能成功求解一维Fokker-Planck方程，求解粒子数为10^5个，能获得十分光滑的PDF分布曲线，计算颗粒在300个时，就能获得较好的均值. 其研究为两相湍流PDF模型新计算方法研究提供基础.

Abstract:Fokker-Planck equation for Stochastic system with whitenoise is reduced to velocity state vector, and the analytic solution of thereduced Fokker-Planck equation is obtained. The hybrid scheme in FiniteAnalytic/Monte Carlo methods is developed to simulate constant parameterscomplete Fokker-Planck equation and complete Fokker-Planck equation withvariable F(X). It is shown that the results obtained from the numericalalgorthm are in good agrement with the analytic solutions, and that thesimulating PDF is smoothed when calculated particles number is 10^5, andthe simulating average moments are about to analytic solutions whencalculated particles number is 300. This work described here is first partof a long-term study in pursuit of a new simulating scheme for two-phaseflows.